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The general results presented above for Hamilton's principle can be applied to optics using the Lagrangian defined in Fermat's principle.The Euler-Lagrange equations with parameter σ =x 3 and N=2 applied to Fermat's principle result in ˙ = with k = 1, 2 and where L is the optical Lagrangian and ˙ = /.
Hamilton's principle states that the true evolution q(t) of a system described by N generalized coordinates q = (q 1, q 2, ..., q N) between two specified states q 1 = q(t 1) and q 2 = q(t 2) at two specified times t 1 and t 2 is a stationary point (a point where the variation is zero) of the action functional [] = ((), ˙ (),) where (, ˙,) is the Lagrangian function for the system.
Hamilton's principle is still valid even if the coordinates L is expressed in are not independent, here r k, but the constraints are still assumed to be holonomic. [37] As always the end points are fixed δr k (t 1) = δr k (t 2) = 0 for all k. What cannot be done is to simply equate the coefficients of δr k to zero because the δr k are not ...
Hamilton's optico-mechanical analogy is a conceptual parallel between trajectories in classical mechanics and wavefronts in optics, introduced by William Rowan Hamilton around 1831. [1] It may be viewed as linking Huygens' principle of optics with Maupertuis' principle of mechanics.
A computer system tracks the patient's eye position 60 to 4,000 times per second, depending on the brand of laser used, redirecting laser pulses for precise placement. Most modern lasers will automatically center on the patient's visual axis and will pause if the eye moves out of range and then resume ablating at that point after the patient's ...
Optical computing or photonic computing uses light waves produced by lasers or incoherent sources for data processing, data storage or data communication for computing.For decades, photons have shown promise to enable a higher bandwidth than the electrons used in conventional computers (see optical fibers).
Numerous other concepts and objects in mechanics, such as Hamilton's principle, Hamilton's principal function, the Hamilton–Jacobi equation, Cayley-Hamilton theorem are named after Hamilton. The Hamiltonian is the name of both a function (classical) and an operator (quantum) in physics, and, in a different sense, a term from graph theory .
A system is focal if an object ray parallel to the axis is conjugate to an image ray that intersects the optical axis. The intersection of the image ray with the optical axis is the focal point F ′ in image space. Focal systems also have an axial object point F such that any ray through F is conjugate to an image ray parallel to the optical axis.